### Theory of Real Functions Tuition Class In Noida

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## Course Objectives:

It is a basic course on the study of real valued functions that would develop
an analytical ability to have a more matured perspective of the key concepts of calculus, namely, limits, continuity, differentiability and their applications. Hence, Join Best Online Math Tutor In Noida.

## Course Learning Outcomes: This course will enable the students to learn

i) To have a rigorous understanding of the concept of limit of a function.
ii) The geometrical properties of continuous functions on closed and bounded intervals.
iii) The applications of mean value theorem and Taylor’s theorem.

## Limits of Functions Tuition

Limits of functions (approach), Sequential criterion for limits, Divergence criteria, Limit theorems, One-sided limits, Infinite limits and limits at infinity. Hence, Limits of Functions Tuition Class In Noida.

## Continuous Functions and their Properties Tuition

Continuous functions, Sequential criterion for continuity and discontinuity, Algebra of continuous functions, Properties of continuous functions on closed and bounded intervals; Uniform continuity, Non-uniform continuity criteria, Uniform continuity theorem. Hence, Continuous Functions and their Properties Tuition Class In Noida.

## Derivability and its Applications Tuition

Differentiability of a function, Algebra of differentiable functions, Carathéodory’s theorem and chain rule; Relative extrema, Interior extremum theorem, Rolle’s theorem, Mean- value theorem and its applications, Intermediate value property of derivatives – Darboux’s theorem. Hence, Derivability and its Applications Tuition Class In Noida.

## Taylor’s Theorem and its Applications Tuition

Taylor polynomial, Taylor’s theorem with Lagrange form of remainder, Application of Taylor’s theorem in error estimation; Relative extrema, and to establish a criterion for convexity; Taylor’s series expansions of , sin x and cos x. Hence, Taylor’s Theorem and its Applications Tuition Class In Noida.

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